What is the squared root of 14400?

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Answer 1 · 2015-12-02T03:10:36

$=color(blue)(120$

$sqrt14400$

We prime factorise the number first (express the number as a product of primes):

$sqrt14400=sqrt(2*2*2*2*2*2*3*3*5*5)$

$=sqrt(2^6 * 3^2 * 5^2)$

$=(2^6 * 3^2 * 5^2)^(color(blue)(1/2$

$=(2^(6*1/2)) * (3^(2*1/2)) * (5^(2*1/2))$

$=color(blue)(2^3*3*5$

$=color(blue)(120$